Confirmatory Factor Analysis
Illustrated Example

[Podcast ~ 9 minutes]

The Scale of Ethnocultural Empathy (SEE) was developed to measure the ethnocultural empathy; that is, the feeling in oneself of other cultures feelings. The SEE consist of four domains measured with nine items. A total of 193 counseling students completed the nine items on the SEE.

SEE Domains
1. Empathic Feelings and Expression (EFE) measured with items efe1, efe2, & efe3
2. Empathic Perspective Taking (EP) measured with items ep1 & ep2
3. Acceptance of Cultural Differences (AC) measured with items ac1 & ac2
4. Empathic Awareness (EA) measured with items ea1 & ea2.

 


LISREL

Step 1

LISREL create many files when it is executed. It is important to create a subdirectory on your hard drive and place all your files in the subdirectory. In this example, I created the following subdirectory on my C drive--

c:\rsch8140

Step 2

Download the following data into your newly created subdirectory

  [SEE Data]--this is an SPSS data file

Step 3

Import the data into LISREL

 

Step 4

You will create a correlation matrix that will be used as the input file for LISREL

Step 5

You will create Simplis syntax (you need to open a Simplis syntax file) to tests your four step model--here is the syntax for the problem

Go to File then New

Then insert the following syntax:

CFA SEE scale 4 factor model
Observed Variables: efe1 efe2 efe3 ep1 ep2 ac1 ac2 ea1 ea2
Correlation Matrix from file c:\rsch8140\see.cor
Sample size = 193


latent variables: EFE EP AC EA
relationships:
efe1 efe2 efe3 = EFE
ep1 ep2 = EP
ac1 ac2 = AC
ea1 ea2 = EA

path diagram
 

Step 6

Run the syntax by clicking on the L icon (top of the screen) 


Output

 efe1 = 0.87*EFE, Errorvar.= 0.24 , Rē = 0.76
(0.060) (0.040)
14.57 6.02

efe2 = 0.87*EFE, Errorvar.= 0.25 , Rē = 0.75
(0.060) (0.041)
14.47 6.14

efe3 = 0.79*EFE, Errorvar.= 0.37 , Rē = 0.63
(0.062) (0.047)
12.73 7.79

ep1 = 0.67*EP, Errorvar.= 0.55 , Rē = 0.45
(0.081) (0.088)
8.30 6.18

ep2 = 0.75*EP, Errorvar.= 0.44 , Rē = 0.56
(0.083) (0.096)
9.00 4.60

ac1 = 0.74*AC, Errorvar.= 0.45 , Rē = 0.55
(0.073) (0.074)
10.15 6.05

ac2 = 0.75*AC, Errorvar.= 0.44 , Rē = 0.56
(0.073) (0.075)
10.21 5.94

ea1 = 0.78*EA, Errorvar.= 0.40 , Rē = 0.60
(0.074) (0.079)
10.45 5.06

ea2 = 0.92*EA, Errorvar.= 0.16 , Rē = 0.84
(0.075) (0.096)
12.23 1.63


Correlation Matrix of Independent Variables

EFE EP AC EA
-------- -------- -------- --------
EFE 1.00

EP 0.61 1.00
(0.07)
8.67

AC 0.72 0.49 1.00
(0.06) (0.09)
12.61 5.54

EA 0.47 0.44 0.52 1.00
(0.07) (0.08) (0.08)
7.00 5.30 6.87

Goodness of Fit Statistics

Degrees of Freedom = 21
Minimum Fit Function Chi-Square = 30.31 (P = 0.086)
Normal Theory Weighted Least Squares Chi-Square = 28.49 (P = 0.13)
Estimated Non-centrality Parameter (NCP) = 7.49
90 Percent Confidence Interval for NCP = (0.0 ; 25.60)

Minimum Fit Function Value = 0.16
Population Discrepancy Function Value (F0) = 0.039
90 Percent Confidence Interval for F0 = (0.0 ; 0.13)
Root Mean Square Error of Approximation (RMSEA) = 0.043
90 Percent Confidence Interval for RMSEA = (0.0 ; 0.080)
P-Value for Test of Close Fit (RMSEA < 0.05) = 0.58

Expected Cross-Validation Index (ECVI) = 0.40
90 Percent Confidence Interval for ECVI = (0.36 ; 0.49)
ECVI for Saturated Model = 0.47
ECVI for Independence Model = 4.18

Chi-Square for Independence Model with 36 Degrees of Freedom = 783.80
Independence AIC = 801.80
Model AIC = 76.49
Saturated AIC = 90.00
Independence CAIC = 840.16
Model CAIC = 178.80
Saturated CAIC = 281.82

Root Mean Square Residual (RMR) = 0.032
Standardized RMR = 0.032
Goodness of Fit Index (GFI) = 0.97
Adjusted Goodness of Fit Index (AGFI) = 0.93
Parsimony Goodness of Fit Index (PGFI) = 0.45

Normed Fit Index (NFI) = 0.96
Non-Normed Fit Index (NNFI) = 0.98
Parsimony Normed Fit Index (PNFI) = 0.56
Comparative Fit Index (CFI) = 0.99
Incremental Fit Index (IFI) = 0.99
Relative Fit Index (RFI) = 0.93

Critical N (CN) = 247.66



Results

[Assumptions not included -- focus on major analysis]

A confirmatory factor analysis was conducted on the four-factor model of the SEE using LISREL. Five indices were used to assess goodness of fit of the model: chi-square, chi-square/df ratio (best if less than 2.0), nonnormed fit index (NNFI, best if .90 or greater), normed fit index (NFI, best if .90 or greater), and root-mean-square error of approximation (RMSEA, best if .05 or less).

A maximum-likelihood method was used to estimate goodness of fit of the four-factor model. The estimation of the initial model suggested that the model was an excellent fit of the data, as indicated by the following indices: χ2(21, N=193)=28.49; χ2 /df = 1.36; NNFI = .98; NFI = .96; RMSEA = .043. In addition, all factor loadings were statistically significant at the p <.01 level suggesting that the four factors were well constructed by the items.